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Board Service Announcements (Altcoins)
Re: Just-Dice.com : Play or Invest : 1% House Edge : Banter++
by
Azlan
on 06/06/2014, 22:00:33 UTC

Consider rolling a 6 sided die until you roll a six.  The expected number of rolls to get a six is 6.


True, but incomplete - according to the small sample bias - rare events (<0.5) go 'unseen' more often then expected when the number of observations is small. Im sure the links offered by others goes into this.

Take your die: You want to roll a six. You roll 6 times. Whats the probability of not seeing the six?
5/6 ^ 6 = 33.48% So a third of the time (with six observations) you will not see the 6 at all.

It gets better. Imagine a 1000 sided die. You bet against the outcome "1000" and you roll exactly 1000 times.
The probability of getting away with it (not seeing the '1000' even once) is 0.999 ^ 999 = 36.8%

Many of your players are implementing this logic with bets with 98% chance of winning. The small sample bias predicts that, in 100 rolls, they will lose less then expected.

Since there is no free sandwich in life you can guess what happens the other 63.2% of the time you roll the 1000 sided die 1000 times..... You will see the rare outcome ('1000') one *or more* times.

Back to a streak of 28 reds (p=0.5). If you expect it to happen 1 in 236M rolls, the small sample bias (relative to the probability) predicts you will see such a steak once *or more* 63% of the time in 236M rolls but wont see it at all ~36% of the time.

M_acchi